Flow over skew side weirs

The classic analytical solution for flows over a side weir—the De Marchi equation—applies only to the special case of Parallel Side Weir in a prismatic channel. Presented here is an analytical solution for flows over a general Skew Side Weir in a nonprismatic channel. The governing equation is derived from the gradually varied flow equation for a rectangular channel with a Skew Side Weir installed on one side, on the assumption that the specific energy of the water remaining in the channel does not vary along the length of the side weir. The governing equation has been successfully solved analytically through a complicated maneuver of integration.; The common Parallel Side Weir is an extreme case of the Skew Side Weir when the downstream channel width approaches the upstream channel width. However, the De Marchi equation cannot be derived directly from the equation for flow over the Skew Side Weir by simply assuming that the channel width approaches uniform, even though the solution of the Skew Side Weir is asymptotically approaching that of the Parallel Side Weir. A general expression for both cases does not exist. In addition, both solutions are expressed in implicit form. Their uses in practical applications are tedious. By non-dimensionalizing the equations of the analytical solution, parametric equations are obtained which relate the dimensionless flow parameters and geometric parameters of the channel and the side weir. Ample design charts based on these parametric equations have been developed for both Parallel Side Weirs and Skew Side Weirs. With these charts, the practical design of side weirs becomes direct and simple. Design procedures are illustrated through design examples.; The validity of analytical solution to the governing side weir equation developed in this research has been verified by numerical solution (Runge-Kutta method). Experiments were set up to test the theory. The experimental results show that for subcritical flow the assumption of constant energy is acceptable. The discharge coefficient of a Skew Side Weir is a function of the ratios of weir height to upstream depth, upstream channel width to upstream depth, and weir length to upstream depth. Analytical results are in good agreement with experimental data.